Space of modular forms of level 605, weight 1, and Character 605.h

• Label: 605.1.h
• Level: $605$
• Weight: $1$
• Character orbit: 605.h
• Rep. character: $\chi_{605}(94,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $66$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	605.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(66\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(605, [\chi])\).

	Total	New	Old
Modular forms	52	36	16
Cusp forms	4	4	0
Eisenstein series	48	32	16

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + q^{4} + q^{5} - q^{9} - q^{16} - q^{20} - q^{25} + 2 q^{31} + q^{36} - 4 q^{45} + q^{49} - 2 q^{59} + q^{64} - 2 q^{71} + q^{80} - q^{81} - 8 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
605.1.h.a	$605$	$1$	605.h	55.h	$10$	$4$	$1$	$0.302$	\(\Q(\zeta_{10})\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)			✓	✓	55.1.d.a	$16$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)